Portfolio Management

CFA Level I — Exam Weight: 8-12%

3

Modules

16

Concepts

9

Formulas

10

Quiz Questions

Key Formulas

8 essential formulas for Portfolio Management.

Utility Function

U = E(R) - ½ × A × σ²

A = risk aversion (A>0: risk-averse)

CAL Equation

E(Rᶜ) = Rᶠ + [E(Rₚ)-Rᶠ]/σₚ × σᶜ

Slope = Sharpe ratio

Portfolio Variance (2 assets)

σ²ₚ = w²ₐσ²ₐ + w²_bσ²_b + 2wₐw_bρσₐσ_b

Diversification when ρ < 1

CAPM

E(Rᵢ) = Rᶠ + βᵢ[E(R_m) - Rᶠ]

Only systematic risk rewarded

Beta

β = Cov(Rᵢ, R_m) / σ²_m

Systematic risk measure

Treynor Ratio

Treynor = (Rₚ - Rᶠ) / βₚ

Return per unit of beta risk

Jensen's Alpha

α = Rₚ - [Rᶠ + β(R_m - Rᶠ)]

Excess return above CAPM

M-squared

M² = (Sharpeₚ - Sharpe_m) × σ_m

Risk-adjusted in return units

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